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In his State of the Union speech last Tuesday, President Obama concluded that "the State of our Union is stronger." The big question is: stronger than what?

Federal debt is a record $12.2 trillion, or 76% of the nation's annual output of goods and services. While that's still well below Greece's 153%, we're headed steadily in the wrong direction.

According to estimates by the Congressional Budget Office, adjusted by Barron's to account for recent tax increases and other factors, if the U.S. doesn't raise taxes further and cut spending dramatically, the national debt could easily reach 153% of economic output by 2035.

These are not just numbers. If the U.S. national debt continues ballooning, we can be sure of a deep, long-lasting recession -- very likely a depression -- sometime in the next two to three decades. The unemployment rate could easily surge to 20%.

Kevin Dietsch / Newscom

The CBO has been issuing warnings about the looming risk of a debt crisis for nearly three years. So far, those warnings have gone unheeded, probably because the crisis seems so far away. But as the CBO keeps pointing out, the longer this particular can gets kicked down the road, the greater the risk that entitlements promised to tens of millions of the old and poor won't be delivered. It could also lead to a fiscal crisis on an unprecedented scale.

This problem can't be solved by asking the rich to pay a little more, despite what the president says. In fact, Barron's calculates that immediately increasing the marginal tax rate to 50% on the top 1% of the country's earners would bring in $500 billion over the next 10 years. This would barely dent the country's debt load, which would then be $20 trillion, and do little to forestall a financial crisis.

Getting the national debt under control will require tax increases for everyone, as well as budget cuts, particularly in entitlement spending, which is beginning to run out of control as the baby boomers hit retirement age. Fixing that now is not an easy task, given that Congress can't even reach a compromise on the current budget deficit (see "A Dangerous Game of Chicken").

The warnings are growing louder. In a July 2010 "Issue Brief" with the ominous title, "Federal Debt and the Risk of a Fiscal Crisis," the CBO cited similar crises in Argentina, Ireland, and Greece as useful comparisons with the one that could hit the U.S. And as recently as last June, the CBO referred to a fiscal crisis in its "Long-Term Budget Outlook," which projected future budgets over decades.

According to the first Brief, a "review of fiscal crises in Argentina, Ireland, and Greece in the past decade reveals instructive common features and differences."

One difference, of course, is that these economies are much smaller and weaker than the powerhouse U.S.'s. So America would presumably cope better with the shock. But one advantage of being small is that it makes you a candidate for bailouts from larger economies. In contrast, the U.S. will be both too big to fail and too big to bail, a potentially toxic combination that could infect all the world's economies.

A key similarity: Argentina, Ireland, and Greece have all been plagued by soaring debt. The U.S. is not there yet. But the CBO warned of the danger that "the surge in debt relative to the country's output would pose a clear threat of a fiscal crisis during the next two decades."

SKEPTICS MIGHT WONDER just how it is possible to make a valid prediction over more than a quarter-century, when it's hard enough to forecast what will happen next year.

Answer: The CBO projections in this chart are not predictions, but scenarios plausible enough to be taken seriously. They show that if certain trends are allowed to continue, the U.S. economy would be under siege.

One key driver of this crisis scenario is inevitable: the aging of the baby boomers. As the chart shows, the rise in the share of the population 65 and over -- the age of eligibility for Medicare -- has just begun. Born from 1946 through 1964, the boomers will range in age from 49 to 67 this year. As they continue to age, the over-65 portion of the population, now 14.1%, will gradually climb, exceeding 20% for the first time in 2029, when the youngest boomers, born in 1964, will be turning 65.

Not coincidentally, around 2029 the ratio of U.S. government debt to annual economic output, or gross domestic product, will begin to exceed its peak of 112.7%, set in 1945, the final year of World War II. The difference, however, is that, with a major war concluded, the expectation then was that U.S. indebtedness would decline. Indeed, by 1955, the ratio had plummeted to 55.5%. In 2029, in contrast, the expectation will be for indebtedness to continue to explode.

The connection between the baby-boomer time bomb and the rising debt-to-GDP ratio reveals that the next 10 years, for all their potential difficulty, are actually the relative calm before the coming storm. And yet the 10-year outlook has framed the current discussion of the debt in Washington. Clearly mindful of this, the CBO's report on the 10-year outlook, released early this month, cautioned that "projections for the period covered in this report do not fully reflect long-term budget pressures," which include "the aging of the population, the rising health-care costs, and…Social Security…."

The CBO added that, "Unless the laws governing those programs are changed -- or the increased spending is accompanied by corresponding reductions in other spending, sufficiently higher tax revenues, or a combination of the two -- debt will rise sharply, relative to GDP, after 2023."

JUST HOW SHARPLY is what the three lines in the chart on this page are meant to approximate. They are based on the Congressional Budget Office's fairly optimistic projections for long-term economic growth, as well as the assumption that "other spending," aside from entitlements, will continue rising at its long-term pace. The CBO's 10-year projection assumes that GDP growth will hit 3.4% by 2014, and accelerate to an annual average of 3.6% from 2015 to 2018.

What about Barron's other assumptions? In his State of the Union address, the president claimed that efforts to tame debt and deficits had already progressed "more than halfway." In his view, then, all that remains to be done is to duplicate what has been done so far. Our assumptions easily accommodate that; in fact, the second and third scenarios, which factor in tax increases, exceed what has been done so far by a wide margin. Yet in all three cases, the long-term trajectory is still daunting.

Barron's calculated these projections by imposing substantial downward revisions on the long-term projections that the CBO published last June. For example, the agency estimated debt-to-GDP at 250% by 2043 in its June 2012 projections. The three new projections Barron's made reduce that ratio to 211%, 203%, and 193%. (For a full explanation of our methodology, see the memo at the end of this story.)

THE ASSUMPTIONS UNDERLYING each projection build on the one before. The top line (blue) incorporates factors that have already reduced the debt, and which fit under the heading of progress already made. They include the end of the payroll-tax holiday early this year; the rise in the marginal rate to 39.6% from 35% on incomes for joint-earners of $450,000 annually and for single-filers of $400,000, and the recent slowdown in the growth of health-care spending, which some regard as temporary, but that the CBO assumes will persist.

The top line also includes the benefit of another factor that the president now opposes: the planned imposition on March 1 of automatic cuts specified in the Budget Control Act of 2011, otherwise known as sequestration. These reductions have been scored by the CBO as worth nearly $1.8 trillion in savings over the next 10 years, a figure that includes a reduction in the cost of debt-servicing. The president wants them replaced by other cuts that he believes would work better.

The second line (green) adds another assumption. It would immediately raise the marginal rate on the top earners to 50% from 39.6%. Obama hasn't proposed such a drastic hike, but our calculations should more than satisfy any lingering view that "millionaires and billionaires" alone could solve the entire problem by paying their "fair share." Remember that most of these rich folks also pay income taxes in their home states.

Assuming that this hike wouldn't alter behavior in such a way as to reduce the tax take -- and ignoring the fact that revenue from the alternative minimum tax would fall as a result -- the additional revenue over 10 years would be a little more than $500 billion. Even throwing in assumed additional savings in debt-servicing costs, the debt reduction wouldn't be huge in proportionate terms. To appreciate the magnitudes involved, the national debt by 2023 would be in the range of $20 trillion, give or take. It shouldn't be surprising that even aggressive tax hikes on the top 1% won't save the day. While the rich do earn a lot, they aren't that numerous.

To raise even more revenue, try rolling back the Bush tax cuts for the other 99%. That would have a 10-year value of three-quarters of a trillion, and even more once we assume reduced debt-servicing costs. That's a big number on its own, but not in relation to our soaring debt. As the third (red) line in the chart shows, the upward trajectory of debt-to-GDP wouldn't be materially altered by such a rollback.

One lesson in this exercise: Unless President Obama proposes drastic spending cuts, his vision for America requires imposing crippling taxes on the very people whose continued prosperity he so strongly champions -- the lower 99%. Even a 25% tax hike on this broad group wouldn't be enough to solve the budget problem unless it was combined with sharp cuts in spending.

Once this becomes clear, things could get ugly. "If the United States encountered a fiscal crisis," observed the CBO in its July 2010 Issue Brief, "the abrupt rise in interest rates would reflect investors' fears that the government would renege on the terms of its existing debt or that it would increase the supply of money to finance its activities or pay creditors and thereby boost inflation."

Add to that nightmare scenario the risk that Uncle Sam would have to renege on promises made to people over 65.

To avoid such scenarios, we need to start right now -- a plea the Congressional Budget Office has been repeating over the years. In its recent report on the 10-year outlook, the agency observed: "Deciding now what policy changes to make to resolve that long-term imbalance would allow for gradual implementation, which would give households, businesses, and state and local governments time to plan and adjust their behavior."

The two main sources for the projections generated by Barron's: the June 2012 Congressional Budget Office report, "The 2012 Long-Term Budget Outlook," which runs numbers going out several decades; and the February 2013 CBO report, "The Budget and Economic Outlook: Fiscal Years 2013-2023."

In all cases, since all figures are essentially back-of-the-envelope approximations, the method followed was to generate estimates that erred on the side of minimizing future estimates of debt to nominal.

The commonly accepted way to measure debt relative to a country's output is to begin with federal debt held by the public (which excludes debt in the government's "trust funds"), and then calculate it as a percentage of current dollar gross domestic product. That's the measure used by the CBO.

In its June 2012 report, the CBO made two long-term projections of debt/GDP, one keying off its "baseline scenario," which is "based on the assumption that current laws generally remain unchanged," the other off its "alternative fiscal scenario," which is based on "current policies" as opposed to "current laws." Barron's chose the more realistic "alternative fiscal scenario."

Those data showed that, by 2043, the debt/GDP ratio would rise to 250% -- a figure so high that CBO analysts decided to stop at that figure and not release figures showing it would rise even further from there, even though it clearly would. On its way to that 250%, the ratio would reach 97% by 2023.

But that 97% was already in need of downward revision. That's because, in the February 2013 10-year projection, the alternative fiscal scenario project the ratio at 87% by 2013 vs. a baseline projection of 77%.

The difference between that 77% and 87% came assuming that "automatic spending reductions established by the Budget Control Act of 2011 (Public Law 112-25) will take effect at the beginning of March, that sharp reductions in Medicare's payment rates for physicians' services will occur at the beginning of January 2014, and that certain tax provisions that have regularly been extended but are set to expire…will expire as scheduled" (pp. 7-8). In other words, by dropping those three assumptions, the 87% figure was generated.

But Barron's wanted to assume that the Budget Control Act of 2011 would take effect at the beginning of March. Figures in Table 1-7 of the Feb. 2013 report (pp. 32-33) showed that of the total dollar value of these three factors, the Budget Control Act accounted for half. Since it accounted for half, that meant the extra 10 percentage points should be cut in half, which meant the 87% CBO projection should scaled down to 82%.

Accordingly, the new alternative fiscal scenario adjusted for the Budget Control Act showed that the debt-GDP ratio would reach 82% by 2023 rather than 97% in the June 2012 projection. Using that downward revision as "anchor," it was calculated that all subsequent figures have to be downwardly revised not by just the difference of 15 percentage points, but proportionately by 82/97 or by 0.845.

Thus, for example, where the June 2012 projection showed debt/GDP at 199% by 2037, that got downwardly revised to 168% (199 x 0.845). Where the June 2012 projection showed debt/GDP at 250% by 2043, that got downwardly revised to 211% (250 x .845).

That data series generated the top (blue) line tracing the trajectory of the debt/GDP ratio. A similar method was followed for the other two lines.

Estimates from the U.S. Treasury for the total tax consequences over 10 years of the Bush tax cuts, combined with estimates from the Joint Committee on Taxation of rescinding the Bush tax cuts for the bottom 99%, were the sources for generating figures used in the second and third trajectories.

Raising the top rate from 35% to 39.6% on the top 1% yielded extra income over 10 years of $240 billion, which came to $52.6 billion for each percentage point of hike ($240/4.6). So raising it by another 10.6 percentage points meant extra revenue of nearly $555 billion. Adding a standard 17% for savings on the cost of debt servicing brings the total reduction of the debt by 2023 to nearly $645 billion.

Since nominal GDP is projected by the CBO at $25.910 trillion by 2023 (Feb. 2013 report, Table 1-1, p. 9), that means every percentage point is worth $259 billion. If we divide $645 billion by $259 billion, we get 2.49 percentage points, which we round up to 3 percentage points.

That means adding the assumption of a tax hike on the top 1% from 39.6% to 50% subtracts another 3 percentage points from the 82% figure we already projected for 2023. We therefore have a new 2023 figure of 79% to compare to the 97% in the June 2012 report.

Again using that 79% as "anchor," it was calculated that all subsequent figures have to be downwardly revised not by just the difference of 18 percentage points, but proportionately by 79/97 or by 0.814.

Thus, for example, where the June 2012 projection showed debt/GDP at 199% by 2037, that got downwardly revised to 162% (199 x 0.814). Where the June 2012 projection showed debt/GDP at 250% by 2043, that got downwardly revised to 203% (250 x .814).

For the third projection, we added the assumption that the Bush tax cuts get immediately rolled back for the bottom 99%, estimated to be worth $762 billion over 10 years. Again adding the extra 17% for the reduced cost of servicing the debt, we get a total debt reduction of $892 billion.

Again, since nominal GDP is projected by the CBO at $25.910 trillion by 2023 (Feb. 2013 report, Table 1-1, p. 9), that means every percentage point is worth $259 billion. If we divide $892 billion by $259 billion, we get 3.44 percentage points, which we round up to 4 percentage points.

That means adding the assumption of rolling back the Bush tax cuts on the bottom 99% subtracts another 4 percentage points from the 82% figure we already projected for 2023. We therefore have a new 2023 figure of 79% to compare to the 97% in the June 2012 report.

Again using that 79% as "anchor," it was calculated that all subsequent figures have to be downwardly revised not by just the difference of 18 percentage points, but proportionately by 75/97 or by 0.773

Thus, for example, where the June 2012 projection showed debt/GDP at 199% by 2037, that got downwardly revised to 154% (199 x 0.773). Where the June 2012 projection showed debt/GDP at 250% by 2043, that got downwardly revised to 193% (250 x 0.773).

The CBO will update its long-term projections in June of this year. These estimates by Barron's are our best guess of what those projections will look like.